The evolutionist terms in the above paragraph are "shows up in" and "gets to be very common in" and "then disappears never to be seen again" and "they end their time in the spotlight."
Really, those are geological terms. Much of that terminology predates the theory of evolution.
Yes, I find the terminology detracts from readability. I guess I never did learn the geological terminology. However, you can find web pages with a pretty good run down on them.
Here is the wikipedia version, and
here is another version you might find easier to follow.
Think of them as names for time periods. Or, if you prefer, think of them as names for
alleged time periods. Dating methods were not well developed at the time these were named. They were viewed as relative time periods, where you could tell which was older even if you could not determine the actual range of dates.
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